Variational Phase Retrieval with Globally Convergent Preconditioned Proximal Algorithm

Huibin Chang*, Stefano Marchesini, Yifei Lou, Tieyong Zeng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

18 Citations (Scopus)
14 Downloads (Pure)


We reformulate the original phase retrieval problem into two variational models (with and without regularization), both containing a globally Lipschitz differentiable term. These two models can be efficiently solved via the proposed Partially Preconditioned Proximal Alternating Linearized Minimization (P3ALM) for masked Fourier measurements. Thanks to the Lipschitz differentiable term, we prove the global convergence of P3ALM for solving the nonconvex phase retrieval problems. Extensive experiments are conducted to show the effectiveness of the proposed methods.

Original languageEnglish
Pages (from-to)56-93
Number of pages38
JournalSIAM Journal on Imaging Sciences
Issue number1
Publication statusPublished - 11 Jan 2018

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Global convergence
  • Partially preconditioned proximal alternating linearized minimization
  • Phase retrieval
  • Poisson/Gaussian noise
  • Regularization
  • Total variation
  • Variational model


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